(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)

Prove that: ((tan theta)/(1-tan theta))-((cot theta)/(1-cot theta))=(cos theta+sin theta)/(cos theta-sin theta)

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)6(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

Let theta in (0,pi/4) and t_(1) = (tan theta)^(tantheta) and t_(2) = (tan theta)^(cottheta),t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta) , then :

(cot theta)/(cot theta-cot3 theta)+(tan theta)/(tan theta-tan3 theta) is equal to

(cot theta)/(cot theta-cot3 theta)+(tan theta)/(tan theta-tan3 theta) is equal to:

Let theta in(0,(pi)/(4)) and t_(1)=(tan theta)^(tan theta),t_(2)=(tan theta)6(cot theta),t_(3)=(cot theta)^(tan theta) and t_(4)=(cot theta)^(cot theta) then